Processes and apparatus of this kind are of use for wrapping palletized loads on their vertical front, side and rear surfaces. A vertical transverse film curtain which extends before the front surface of the load from two film reels having stationary vertical spindles and disposed on either side of a powered conveyor carrying the load, is first produced by means of a transverse weld. The load moves towards the curtain. The curtain is deformed transversely substantially into a substantially U-shaped contour to cover the front and side surfaces of the load. The same stops when it has passed the reels. The curtain is deformed transversely on either side of the load to apply the film to the rear surface so as to be closed on itself. By means of cutting and welding jaws the curtain is cut and double-welded transversely to disconnect the wrapped load from the film coming off the reels and to restore a film curtain for a subsequent wrapping cycle for another load.